The 33-year-old's existing deal at Camp Nou is due to expire next June, and there have been suggestions that the Argentina international could seek pastures new at the end of next season.
Messi was hugely critical of Barca in the aftermath of their 2-1 loss to Osasuna on July 16, with the Catalan giants conceding this season's La Liga title to Real Madrid.
The South American has enjoyed another excellent campaign at club level, scoring 30 times and contributing 26 assists in 42 appearances in all competitions.
Inter were recently credited with an interest in Messi, and according to Gazzetta dello Sport, the Italian giants will attempt to bring him to San Siro next summer.
The report claims that Inter are confident of turning the attacker's head with the offer of a big-money contract, while a fresh challenge in a new league could also appeal to the Argentine.
Messi has scored 633 goals in 729 appearances for Barca in all competitions.